{"id":"https://openalex.org/W1973085268","doi":"https://doi.org/10.1137/s0036142900379461","title":"Least-Squares Galerkin Methods for Parabolic Problems II: The Fully Discrete Case and Adaptive Algorithms","display_name":"Least-Squares Galerkin Methods for Parabolic Problems II: The Fully Discrete Case and Adaptive Algorithms","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1973085268","doi":"https://doi.org/10.1137/s0036142900379461","mag":"1973085268"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142900379461","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900379461","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051984513","display_name":"Mohammad Majidi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mohammad Majidi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5066679330","display_name":"Gerhard Starke","orcid":"https://orcid.org/0000-0001-5985-173X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gerhard Starke","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.859,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.83315903,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"39","issue":"5","first_page":"1648","last_page":"1666"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.857079267501831},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7766517400741577},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6392087936401367},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5996898412704468},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.49405959248542786},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4928765296936035},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.4762064218521118},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.46881794929504395},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.4258943498134613},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37204480171203613},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3579176962375641},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31253349781036377},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3019772469997406},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13127660751342773},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06665199995040894}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.857079267501831},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7766517400741577},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6392087936401367},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5996898412704468},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.49405959248542786},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4928765296936035},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4762064218521118},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.46881794929504395},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.4258943498134613},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37204480171203613},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3579176962375641},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31253349781036377},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3019772469997406},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13127660751342773},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06665199995040894},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142900379461","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142900379461","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.24.1371","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.1371","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ifam.uni-hannover.de/~starke/papers/timelsq2.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W75801351","https://openalex.org/W1492326914","https://openalex.org/W1972792313","https://openalex.org/W1990409988","https://openalex.org/W1995504856","https://openalex.org/W2006810111","https://openalex.org/W2038626747","https://openalex.org/W2068363147","https://openalex.org/W2071036364","https://openalex.org/W2082621526","https://openalex.org/W2094875449","https://openalex.org/W2163694039","https://openalex.org/W3209416867","https://openalex.org/W4241914827","https://openalex.org/W4242273588","https://openalex.org/W4255754126","https://openalex.org/W4292166829"],"related_works":["https://openalex.org/W2355560061","https://openalex.org/W1996322735","https://openalex.org/W1978749675","https://openalex.org/W2613898712","https://openalex.org/W2080994790","https://openalex.org/W2119544289","https://openalex.org/W2041896318","https://openalex.org/W1991960225","https://openalex.org/W4309798349","https://openalex.org/W2782024549"],"abstract_inverted_index":{"In":[0],"this":[1],"second":[2],"part":[3],"of":[4,32,55,119,137,169],"our":[5],"series":[6],"on":[7,29,52,115],"least-squares":[8,34],"Galerkin":[9],"methods":[10,26],"for":[11,36,72,143,147],"parabolic":[12],"initial-boundary":[13],"value":[14],"problems":[15],"we":[16,66,87],"study":[17],"the":[18,30,53,56,63,73,83,96,116,120,126,130,138,149,153,167,170],"full":[19],"discretization":[20,85],"in":[21,58,62,125,174],"time":[22,44,59,79,175],"and":[23,43,80,108,112,129,135,152,176],"space.":[24,81,177],"These":[25],"are":[27],"based":[28],"minimization":[31,98],"a":[33,68,89,102,113,157],"functional":[35,97],"an":[37,144],"equivalent":[38],"first-order":[39],"system":[40],"over":[41],"space":[42,84,111],"with":[45,78,93],"respect":[46,94],"to":[47,95],"suitable":[48],"discrete":[49],"spaces.":[50],"Based":[51],"analysis":[54],"semi-discretization":[57],"carried":[60],"out":[61],"first":[64],"part,":[65],"construct":[67],"posteriori":[69],"error":[70,75,86,139],"estimators":[71],"approximation":[74],"components":[76],"associated":[77],"For":[82],"use":[88],"hierarchical":[90,109],"basis":[91],"estimator":[92],"problem.":[99],"We":[100],"prove":[101],"strengthened":[103],"Cauchy--Schwarz":[104],"inequality":[105],"between":[106,160],"coarse":[107],"surplus":[110],"bound":[114],"condition":[117],"number":[118],"auxiliary":[121],"problem,":[122],"both":[123,148],"uniform":[124],"mesh-size":[127],"h":[128],"time-step":[131,150],"$\\tau$":[132],"implying":[133],"efficiency":[134],"reliability":[136],"estimator.":[140],"This":[141],"allows":[142],"adaptive":[145,172],"strategy":[146],"size":[151],"spatial":[154],"triangulation,":[155],"keeping":[156],"proper":[158],"balance":[159],"these":[161],"two":[162],"components.":[163],"Numerical":[164],"experiments":[165],"illustrate":[166],"performance":[168],"resulting":[171],"schemes":[173]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
